Related papers: Dynamical Triangulations, a Gateway to Quantum Gra…
It is shown that application of dynamic flows concept in 4-dimensional Euclidean space makes possible to form Minkowski space and to formulate the generalized variational problem of electrodynamics and gravi- dynamics. It is shown that…
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…
Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the…
We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general…
We consider the quantum dynamics of both open and closed two- dimensional universes with ``wormholes'' and particles. The wave function is given as a sum of freely propagating amplitudes, emitted from a network of mapping class images of…
The four dimensional Causal Dynamical Triangulations (CDT) approach to quantum gravity is already more than ten years old theory with numerous unprecedented predictions such as non-trivial phase structure of gravitational field and…
In Hawking's Euclidean path integral approach to quantum gravity, the partition function is computed by summing contributions from all possible topologies. The behavior such a sum can be estimated in three spacetime dimensions in the limit…
We search for a continuum limit in the causal dynamical triangulation (CDT) approach to quantum gravity by determining the change in lattice spacing using two independent methods. The two methods yield similar results that may indicate how…
In this paper explore the relation between covariant and canonical approaches to quantum gravity and $BF$ theory. We will focus on the dynamical triangulation and spin-foam models, which have in common that they can be defined in terms of…
I discuss a model for quantized gravitation based on the simplicial lattice discretization. It has been studied in some detail using a comprehensive finite size scaling analysis combined with renormalization group methods. The results are…
A new exact renormalization group equation for the effective average action of Euclidean quantum gravity is constructed. It is formulated in terms of the component fields appearing in the transverse-traceless decomposition of the metric. It…
We obtain a dynamical formulation of two-dimensional gravity from a non-Einsteinian phase in higher dimensions $(D=3+2n)$. The formalism is associated with (at least) one extra dimension of vanishing proper length, thus being inequivalent…
A block spin renormalization group approach is proposed for the dynamical triangulation formulation of quantum gravity in arbitrary dimensions. Renormalization group flow diagrams are presented for the three-dimensional and four-dimensional…
Known quantum and classical perturbative long-distance corrections to the Newton potential are extended into the short-distance regime using evolution equations for a `running' gravitational coupling, which is used to construct examples…
The first computation of a spin foam dynamics that provides a test of the quantum equations of motions of gravity is presented. Specifically, a triangulation that includes an inner edge is treated. The computation leverages the recently…
We perform the two loop level renormalization of quantum gravity in $2+\epsilon$ dimensions. We work in the background gauge whose manifest covariance enables us to use the short distance expansion of the Green's functions. We explicitly…
We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to…
We give a review of recent work aimed at understanding the dynamics of gravitational collapse in quantum gravity. Its goal is to provide a non-perturbative computational framework for understanding the emergence of the semi-classical…
The spectral dimension measures the dimensionality of a space as witnessed by a diffusing random walker. Within the causal dynamical triangulations approach to the quantization of gravity, the spectral dimension exhibits novel…
We investigate quantum gravity in four dimensions using the Regge approach on triangulations of the four-torus with general, non-regular incidence matrices. We find that the simplicial lattice tends to develop spikes for vertices with low…